Whakaoti i te 3x-4/7+7/3x-4=5/2.xneq4/3

$$\frac { 3 x - 4 } { 7 } + \frac { 7 } { 3 x - 4 } = \frac { 5 } { 2 } . x \neq \frac { 4 } { 3 }$$

Whakaoti mō x

$$x=6$$

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki \frac{4}{3} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 14\left(3x-4\right), arā, te tauraro pātahi he tino iti rawa te kitea o 7,3x-4,2.

$$\left(6x-8\right)\left(3x-4\right)+14\times 7=35\left(3x-4\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 6x-8 ki te 3x-4 ka whakakotahi i ngā kupu rite.

$$18x^{2}-48x+32+14\times 7=35\left(3x-4\right)$$

Whakareatia te 14 ki te 7, ka 98.

$$18x^{2}-48x+32+98=35\left(3x-4\right)$$

Tāpirihia te 32 ki te 98, ka 130.

$$18x^{2}-48x+130=35\left(3x-4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 35 ki te 3x-4.

$$18x^{2}-48x+130=105x-140$$

Tangohia te 105x mai i ngā taha e rua.

$$18x^{2}-48x+130-105x=-140$$

Pahekotia te -48x me -105x, ka -153x.

$$18x^{2}-153x+130=-140$$

Me tāpiri te 140 ki ngā taha e rua.

$$18x^{2}-153x+130+140=0$$

Tāpirihia te 130 ki te 140, ka 270.

$$18x^{2}-153x+270=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 18 mō a, -153 mō b, me 270 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-153\right)±\sqrt{\left(-153\right)^{2}-4\times 18\times 270}}{2\times 18}$$

Pūrua -153.

$$x=\frac{-\left(-153\right)±\sqrt{23409-4\times 18\times 270}}{2\times 18}$$

Whakareatia -4 ki te 18.

$$x=\frac{-\left(-153\right)±\sqrt{23409-72\times 270}}{2\times 18}$$

Whakareatia -72 ki te 270.

$$x=\frac{-\left(-153\right)±\sqrt{23409-19440}}{2\times 18}$$

Tāpiri 23409 ki te -19440.

$$x=\frac{-\left(-153\right)±\sqrt{3969}}{2\times 18}$$

Tuhia te pūtakerua o te 3969.

$$x=\frac{-\left(-153\right)±63}{2\times 18}$$

Ko te tauaro o -153 ko 153.

$$x=\frac{153±63}{2\times 18}$$

Whakareatia 2 ki te 18.

$$x=\frac{153±63}{36}$$

Nā, me whakaoti te whārite x=\frac{153±63}{36} ina he tāpiri te ±. Tāpiri 153 ki te 63.

$$x=\frac{216}{36}$$

Whakawehe 216 ki te 36.

$$x=6$$

Nā, me whakaoti te whārite x=\frac{153±63}{36} ina he tango te ±. Tango 63 mai i 153.

$$x=\frac{90}{36}$$

Whakahekea te hautanga \frac{90}{36} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 18.

$$x=\frac{5}{2}$$

Kua oti te whārite te whakatau.

$$x=6 x=\frac{5}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki \frac{4}{3} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 14\left(3x-4\right), arā, te tauraro pātahi he tino iti rawa te kitea o 7,3x-4,2.

$$\left(6x-8\right)\left(3x-4\right)+14\times 7=35\left(3x-4\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 6x-8 ki te 3x-4 ka whakakotahi i ngā kupu rite.

$$18x^{2}-48x+32+14\times 7=35\left(3x-4\right)$$

Whakareatia te 14 ki te 7, ka 98.

$$18x^{2}-48x+32+98=35\left(3x-4\right)$$

Tāpirihia te 32 ki te 98, ka 130.

$$18x^{2}-48x+130=35\left(3x-4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 35 ki te 3x-4.

$$18x^{2}-48x+130=105x-140$$

Tangohia te 105x mai i ngā taha e rua.

$$18x^{2}-48x+130-105x=-140$$

Pahekotia te -48x me -105x, ka -153x.

$$18x^{2}-153x+130=-140$$

Tangohia te 130 mai i ngā taha e rua.

$$18x^{2}-153x=-140-130$$

Tangohia te 130 i te -140, ka -270.

$$18x^{2}-153x=-270$$

Whakawehea ngā taha e rua ki te 18.

$$\frac{18x^{2}-153x}{18}=-\frac{270}{18}$$

Mā te whakawehe ki te 18 ka wetekia te whakareanga ki te 18.

$$x^{2}+\left(-\frac{153}{18}\right)x=-\frac{270}{18}$$

Whakahekea te hautanga \frac{-153}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 9.

$$x^{2}-\frac{17}{2}x=-\frac{270}{18}$$

Whakawehe -270 ki te 18.

$$x^{2}-\frac{17}{2}x=-15$$

Whakawehea te -\frac{17}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{17}{4}. Nā, tāpiria te pūrua o te -\frac{17}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{17}{2}x+\left(-\frac{17}{4}\right)^{2}=-15+\left(-\frac{17}{4}\right)^{2}$$

Pūruatia -\frac{17}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{17}{2}x+\frac{289}{16}=-15+\frac{289}{16}$$

Tāpiri -15 ki te \frac{289}{16}.

$$x^{2}-\frac{17}{2}x+\frac{289}{16}=\frac{49}{16}$$

Tauwehea x^{2}-\frac{17}{2}x+\frac{289}{16}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{17}{4}\right)^{2}=\frac{49}{16}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x-\frac{17}{4}\right)^{2}}=\sqrt{\frac{49}{16}}$$

Whakarūnātia.

$$x-\frac{17}{4}=\frac{7}{4} x-\frac{17}{4}=-\frac{7}{4}$$

Me tāpiri \frac{17}{4} ki ngā taha e rua o te whārite.

$$x=6 x=\frac{5}{2}$$